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id	challengeType	title	forumTopicId
5900f3ae1000cf542c50fec1	5	Problem 66: Diophantine equation	302178

Description

Consider quadratic Diophantine equations of the form: x2 – Dy2 = 1 For example, when D=13, the minimal solution in x is 6492 – 13×1802 = 1. It can be assumed that there are no solutions in positive integers when D is square. By finding minimal solutions in x for D = {2, 3, 5, 6, 7}, we obtain the following: 32 – 2×22 = 1 22 – 3×12 = 192 – 5×42 = 1 52 – 6×22 = 1 82 – 7×32 = 1 Hence, by considering minimal solutions in x for D ≤ 7, the largest x is obtained when D=5. Find the value of D ≤ 1000 in minimal solutions of x for which the largest value of x is obtained.

Instructions

Tests

tests:
  - text: <code>euler66()</code> should return 661.
    testString: assert.strictEqual(euler66(), 661);

Challenge Seed

function euler66() {
  // Good luck!
  return true;
}

euler66();

Solution

// solution required

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